For virtual musical instruments and audio effects, the model
replaces the real thing. Therefore, the model's
prediction from its inputs (controls and possible input
sounds), is simply the desired output sound. Since a sound is a
special case of a signal, we can say that all models of
interest in this book are signal models.

Also in the musical case, we often desire that our models run in
real time. That is, we may supply model inputs from a live
human performer, and the task of the model becomes rendering
high-quality sound based on performance gestures. Real-time
computational forms are ubiquitous in the field of digital signal
processing, and in large measure, this book is about signal
processing methods most applicable to real-time computational physical models.

Physical models are desirable when many dimensions of expressive
control are needed. This is generally best appreciated by
performing musicians. Audience members only hear the final
music played, so they are not in a position to judge the quality of
multidimensional control, as skilled musicians utilize only a narrow
control subspace in any given performance.2.1